Journal of Differential Geometry

Integrated Harnack inequalities on Lie groups

Bruce K. Driver and Maria Gordina

Full-text: Open access

Abstract

We show that the logarithmic derivatives of the convolution heat kernels on a uni-modular Lie group are exponentially integrable. This result is then used to prove an “integrated” Harnack inequality for these heat kernels. It is shown that this integrated Harnack inequality is equivalent to a version of Wang’s Harnack inequality. (A key feature of all of these inequalities is that they are dimension independent.) Finally, we show these inequalities imply quasi-invariance properties of heat kernel measures for two classes of infinite dimensional “Lie” groups.

Article information

Source
J. Differential Geom., Volume 83, Number 3 (2009), 501-550.

Dates
First available in Project Euclid: 27 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1264601034

Digital Object Identifier
doi:10.4310/jdg/1264601034

Mathematical Reviews number (MathSciNet)
MR2581356

Zentralblatt MATH identifier
1205.53044

Citation

Driver, Bruce K.; Gordina, Maria. Integrated Harnack inequalities on Lie groups. J. Differential Geom. 83 (2009), no. 3, 501--550. doi:10.4310/jdg/1264601034. https://projecteuclid.org/euclid.jdg/1264601034


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